I'm analyzing a set of biological samples. Each sample is linked to a specific carbon and nitrogen concentration, representing the 2D (experimental) design space I referenced in the title. I've measured 20 metabolites for each sample. Initially, I used standard correlation/PCA analysis for this multivariate data. However, for this approach, I ignored the carbon/nitrogen coordinates. What methods can I employ to compare the samples while incorporating the C/N coordinates, i.e., the structure of the design space?